A generalised beta integral and the limit of the Bernstein--Durrmeyer operator with Jacobi weights

DOI10.1016/S0021-9045(03)00041-8zbMath1024.41014MaRDI QIDQ1810601

Shayne F. D. Waldron

Publication date: 9 June 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

zbMATH Keywords

Jacobi polynomialsBernstein-Durrmeyer operatormultivariate beta integral

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Eigenvalue problems for linear operators (47A75) Linear operators on function spaces (general) (47B38) Approximation by operators (in particular, by integral operators) (41A35)

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Cites Work

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• On multivariate approximation by Bernstein-type polynomials
• Sur l'approximation de fonctions intégrables sur l'interval-0,1-ferme par des polynômes de Bernstein modifies
• The genuine Bernstein-Durrmmeyer operator on a simplex
• The approximation of the continuous functions by means of some linear positive operators